I have gone through this but on the flipside. I dated a guy I really liked, he was quite a bit younger than me, but eventually became jealous and possesive - so much that I left him.
My take on it is this: Falling for someone opens you up to getting hurt, you take a risk by allowing yourself to feel that emotion. A mature relationship involves honesty and trust so that both parties feel safe putting their hearts in the hands of the other person and trusting that the other person won't take advantage of that trust and hurt them - intentionally or unintentionally.
Jealousy and possesiveness stem from your insecurities, not her actions. If she hasn't given you a reason to think suspicious thoughts of her then the cause of your jealousy is your insecurity, which you have admitted to. My advice is to do some serious self-analysis. There is no shame in admitting that you feel this way, so look at yourself honestly. Why do you feel you don't measure up? What is the root of these feelings? Is it with women in general or just with her? Does it stem from childhood, from something your mother did to your father?
You mentioned that a past girlfriend had hurt you, you have to deal with that anger and find a way to forgive her, forgive yourself and let it go. You have to be healthy and love yourself before you can have a healthy relationship and love someone else.
Further, why not try talking to her about your feelings? Don't be accusatory, just tell her that you're really into her and maybe she can reassure you that she's into you too and alleviate some of your fears. Don't be possesive, trust me, I really liked this guy but there's no bigger turn-off than being suspected of cheating every time you leave the house. I can also tell you that if you don't come to terms with these feelings now, and find a way to overcome it, it will get worse and worse the more you care about her and eventually push her away or keep her prisoner - neither of which you want, I'm sure - then it will become a habit and haunt you throughout your relationships.
It's good that you recognize it and seek help now. Good luck, hope I've been helpful.